Posted: June 17th, 2016

Draw the pmf of the Poisson distribution that results when the parameter α is equal to the following: (a) α = 1/2 (b) α = 1 (c) α = 2 (d) α = 4

. Draw the pmf of the Poisson distribution that results when the parameter α is equal to the following:
(a) α = 1/2
(b) α = 1
(c) α = 2
(d) α = 4
10. On one figure, draw the two exponential pdfs that result when the parameter λ equals 0.6 and 1.2.
11. On one figure, draw the three Weibull pdfs that result when ν = 0, α = 1/2, and β = 1, 2, and 4.

10.1

A simulation model of a job shop was developed to investigate different scheduling rules. To validate the model, the scheduling rule currently used was incorporated into the model and the resulting output was compared against observed system behavior. By searching the previous year’s database records, it was estimated that the average number of jobs in the shop was 22.5 on a given day. Seven independent replications of the model were run, each of 30 days’ duration, with the following results for average number of jobs in the shop:

1 8.9 22.0 19.4 22.1 19.8 21.9 20.2

a. Develop and conduct a statistical test to evaluate whether model output is consistent with system behavior. Use the level of significance α = 0.05.

b. What is the power of this test if a difference of two jobs is viewed as critical? What sample size is needed to guarantee a power of 0.8 or higher? (Use α = 0.05.)

11.1
A store selling Mother’s Day cards must decide 6 months in advance on the number of cards to stock. Reordering is not allowed. Cards cost $0.45 and sell for $1.25. Any cards not sold by Mother’s Day go on sale for $0.50 for 2 weeks. However, sales of the remaining cards is probabilistic in nature according to the following distribution:

32% of the time, all cards remaining get sold.

40% of the time, 80% of all cards remaining are sold.

28% of the time, 60% of all cards remaining are sold.

Any cards left after 2 weeks are sold for $0.25. The card-shop owner is not sure how many cards can be sold, but thinks it is somewhere (i.e., uniformly distributed) between 200 and 400. Suppose that the card-shop owner decides to order 300 cards. Estimate the expected total profit with an error of at most $5.00. [Hint: Make ten initial replications. Use these data to estimate the total sample size needed. Each replication consists of one Mother’s Day.]